If a player triggers a shuffle during the action phase (not by camping), they must return to San Andreas immediately.

This is supported by the following rules:

• On page 13:
  "At any time, if your personal deck is empty and you need to draw a card or reveal a card from the top of your deck, reshuffle your discard pile to replenish your deck. When this occurs, you must return your character to San Andreas."

• On page 23:
  "If you shuffled your deck at any point during this past round other than by taking the camp action, return your figure to San Andreas. This includes a reshuffle as a result of the Redraw step."

The rule on page 13 uses the phrase "at any time," indicating that the return to San Andreas is immediate upon shuffling, regardless of the phase or action being performed, unless the shuffle was caused by the camp action (which is an exception).

Summary

A player who triggers a shuffle during the action phase (not by camping) must immediately return to San Andreas, interrupting their current action.

Sources:
Page 13, Page 23

Source: Core Rulebook (pp. 13, 20, 22, 23, 32)